For a good that is a luxury, which statement best describes demand when consumer income rises?

• A. Demand increases by a smaller percentage than income (income elasticity of demand $0<E{I}_D<1$).
• B. Demand does not change when income changes (income elasticity of demand $E{I}_D=0$).
• C. Demand decreases as income rises (income elasticity of demand $E{I}_D<0$).
• D. Demand increases by a greater percentage than income (income elasticity of demand $E{I}_D>1$).

Answer: (D)

Verified step by step guidance

1. Understand the concept of income elasticity of demand, which measures how the quantity demanded of a good responds to a change in consumer income. It is calculated as \(E_{ID} = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in income}}\).
2. Recall that for normal goods, the income elasticity of demand is positive, meaning demand increases as income rises.
3. Identify that luxury goods are a special type of normal goods where demand increases more than proportionally as income rises, implying an income elasticity of demand greater than 1.
4. Analyze the given options by comparing their income elasticity values: less than 0 (inferior goods), equal to 0 (no change in demand), between 0 and 1 (normal but not luxury), and greater than 1 (luxury goods).
5. Conclude that for a luxury good, the correct description is that demand increases by a greater percentage than income, which corresponds to an income elasticity of demand \(E_{ID} > 1\).